In this exercise you will develop an econometric model to forecast unemployment. The data file USMacro_Quarterly contains data on the unemployment rate from the Federal Reserve Bank of St. Louis. A more detailed description is given in USMacro_Quarterly description.

1. Plot a graph of unrate. Based on the plot, does it look like unrate follows a stochastic trend?
2. Compute the first eight autocorrelations of unrate. Does this look like a highly persistent time series?In all estimations that follow below, restrict your data to begin in quarter 1 of 1960. (That way you can make sure that you get the same numbers of observations no matter what lag length you are choosing.) Also, do not include a deterministic time trend in your estimations.
3. Test unrate for a unit root. Make sure you are using an optimal number of lags when you test for unit root. Use both the AIC and the BIC to determine the lag order. In case they give you different answers, use the lag order that is suggested by the AIC. Try lags up to order 8. (When you test for unit root, do not include a deterministic trend.)
4. Estimate an AR(2) model for unrate. Use that model to predict the level of unemployment in 2014:Q1.
5. Estimate an AR(2) model for Dunrate (the first difference in unrate). Use that model to predict the level of unemployment in 2014:Q1.
6. In light of your answer to part c) above, which unemployment forecast do your prefer? The one from part d) or the one from part e)?